Dawn is definitely the cheaper of the two. I use S100 Shine-enhancing Cleanser. Get it for $9.00 at your local Harley shop. As the ad says, "an easy-to-apply pure polish for all painted surfaces. It improves surface gloss by removing old wax, minor spotting and swirl lines."
You'll want to Dawn wash after S100, if you're going the way of the Z.